International Journal of Scientific Engineering and Technology Volume 2 Issue 4, pp : 185-191 In this problem, chromosomes are constituted via binary coding systems. Since the design variables are discrete, it is necessary to prepare a pool of possible design variables, which may be assumed as design variables. The design variables pool considered is as follows: (As per SP 6 part 1) S = {ISWB 150, ISWB 175, ISWB 200, ISWB 225, ISWB 250, ISWB 300, ISWB 350, ISWB 400, ISWB 450, ISWB 500, ISWB 550, ISWB 600, ISHB 150, ISHB 200, ISHB 225, ISHB 250, ISHB 300, ISHB 350, ISHB 400, ISHB 450} OR in terms of area of the sections (cm2) involved in population pool. S={21.67, 28.11, 39.71, 43.25, 52.05, 61.33, 72.50, 85.01, 101.15, 121.22, 143.34, 170.38, 184.86, 34.48, 38.98, 44.08, 47.54, 50.94, 54.94, 59.66, 64.96, 69.71, 74.85, 80.25, 85.91, 92.21, 98.66, 104.66, 111.14, 117.89}. The optimization was performed by the proposed Genetic algorithm optimization approach. The task of the optimization was to find the minimal structure’s material and labour costs, the optimal topology with the optimal number of portal frames and purlins as well as the optimal standard cross-sections of members. The economical objective function included the material, anti-corrosion and fire (R 30) protection painting as well as assembling and erection costs of the structure. The economic data for the optimization are presented in Table 1. The fabrication costs of steel elements were calculated to be equal to 40% of the obtained material costs (Cfabr = 0.40). Table 1 Economic Data for optimization (Courtesy MFF Hazira, L&T Powai) Cmat Price of the structural steel 1.05 EUR/kg Cpaint Anti-corrosion resistant 22.5 EUR/m2 painting costs (R30) Cerect,frame Erection costs per 1 portal 450 EUR/frame frame Cerect,purlin Erection costs per 1 purlin 250 EUR/purlin
(ISSN : 2277-1581) 1 April 2013
Frames
Purlins
Beams
Columns
Purlins
13.2 15 13 14 14
11.6 12 16 12 14
121.22 121.22 121.22 121.22 121.22
184.86 184.86 184.86 184.86 184.86
36.71 36.71 36.71 36.71 36.71
cost (EUR) 16445.821 18315.477 17478.508 17337.235 17890.685
Fig 4 Optimum design of portal steel frame The optimal result represented the obtained structure’s minimal material and labour costs of 17337.235 EUR. The selling price may be at least twice higher. The solution also comprised the calculated optimal topology of 14 portal frames and 12 purlins, see Fig. 5, and the calculated optimal standard sections of columns (ISWB 600@145.1 kg/m), beams (ISWB 500@95.2 kg/m) and purlins (ISWB 200@28.8 kg/m), see Fig. 4. The obtained structure mass was 76120.34 kg.
IV. Results and Discussion The optimization was carried out by user-friendly version of GATOOL-BOX incorporated in MATLAB and computer program written in C-Language. Also to investigate the viability of using genetic algorithms for design optimization of structural systems and to show whether the developed program is compatible, a 10-bar truss (one problem taken from literature) is solved and the results obtained are compared to various other optimization algorithm. Results obtained from running the program are as follows: Table 2 Results obtained from C program Topology
Cross sectional areas (cm2)
Frames
Purlins
Beams
Columns
Purlins
15 13 14 14
12 16 12 14
121.22 121.22 121.22 121.22
184.86 184.86 184.86 184.86
36.71 36.71 36.71 36.71
Resultant cost (EUR) 18315.5 17478.5 17337.2 17890.7
Table 3 Results obtained from MATLAB Topology
IJSET@2013
Cross sectional areas (cm2)
Resultant
Fig. 5 Optimum design of single storey industrial steel building The optimal result represented the obtained structure’s minimal material and labour costs of 17337.235 EUR. The selling price may be at least twice higher. The solution also comprised the calculated optimal topology of 14 portal frames and 12 purlins, see Fig. 5, and the calculated optimal standard sections of columns (ISWB 600@145.1 kg/m), beams (ISWB 500@95.2 kg/m) and purlins (ISWB 200@28.8 kg/m), see Fig. 4. The obtained structure mass was 76120.34 kg.
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